A generalization of the forward-reflected-backward splitting method for monotone inclusions

In this paper, we propose a general forward-reflected-backward splitting method for solving monotone inclusions in Hilbert spaces. Our method extends and improves the one of Malitsky and Tam (SIAM J. Optim., 2020). The weak convergence of the proposed algorithm is established under standard conditions. The linear convergence of the proposed method is derived under an additional condition like the strong monotonicity. We also give some theoretical comparisons to demonstrate the efficiency of the proposed algorithm.